01477043

Component

The objectives of this study are to: 1) examine the applicability of the double Poisson (DP) generalized linear model (GLM) for analyzing motor vehicle crash data characterized by over- and under-dispersion and 2) compare the performance of the DP GLM with the Conway-Maxwell-Poisson (COM-Poisson) GLM in terms of goodness-of-fit and theoretical soundness. The DP distribution has seldom been investigated and applied since its first introduction two decades ago. The hurdle of applying the DP is related to its normalizing constant (or multiplicative constant) which is not available in closed form. This study proposed a new method to approximate the normalizing constant of the DP with high accuracy and reliability. The DP GLM and COM-Poisson GLM were developed using two observed over-dispersed datasets and one simulated under-dispersed dataset. The performances of the negative binomial (NB) GLM (for over-dispersion) and Poisson GLM (for under-dispersion) were also provided as reference. The modeling results indicate that the DP GLM with its normalizing constant approximated by the new method can handle crash data characterized by over- and under-dispersion. Its performance is comparable to the COM-Poisson GLM in terms of goodness-of-fit (GOF), although COM-Poisson GLM provides a slightly better fit. For the over-dispersed data, the DP GLM performs similar to the NB GLM. This study also shows that the traditional Poisson GLM overestimates the standard errors of the coefficients when the data are characterized by under-dispersion. Considering the fact that the DP GLM can be easily estimated and computationally inexpensive, it offers a flexible and efficient alternative for researchers to model the count data.

This paper was sponsored by TRB committee ABJ80 Statistical Methods.

01470560

13-2138

English

18p

2013

Transportation Research Board 92nd Annual Meeting

Digital/other

References; Tables

Crash data; Crash rates; Linear equations; Poisson distributions; Statistical analysis; Traffic crashes

Highways; Safety and Human Factors; I80: Accident Studies; I81: Accident Statistics

Transportation Research Board Annual Meeting 2013 Paper #13-2138

TRIS, TRB, ATRI

Feb 5 2013 12:29PM